Crossing Angles of Geometric Graphs

  • Karin Arikushi
  • Csaba D. Tóth
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7402)


We study the crossing angles of geometric graphs in the plane. We introduce the crossing angle number of a graph G, denoted can(G), which is the minimum number of angles between crossing edges in a straight line drawing of G. We show that an n-vertex graph G with can(G) = O(1) has O(n) edges, but there are graphs G with bounded degree and arbitrarily large can(G). We also initiate studying the global crossing-angle rigidity of geometric graphs. We construct bounded degree graphs G = (V,E) such that for any two straight-line drawings of G with the same prescribed crossing angles, there is a subset V′ ⊂ V of |V′| ≥ |V|/2 vertices that are similar in the two drawings.


Complete Graph Supporting Line Geometric Graph Free Vertex Geometric Thickness 
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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Karin Arikushi
    • 1
  • Csaba D. Tóth
    • 1
  1. 1.Department of Mathematics and StatisticsUniversity of CalgaryCalgaryCanada

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